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An autonomous construction system (ACS) is envisioned to be a solution to the construction of structures in environments that are too hazardous for humans and where remote operation is not possible. Drawing inspiration from the construction behavior of social insects, we advance the state of the art by proposing a completely decentralized control strategy for a multi-robot ACS. This control strategy is based on previous work by Theraulaz and Bonabeau, who demonstrated multi-agent construction using a three-dimensional lattice-based simulation. In order to study the proposed decentralized control strategy, we set about designing a multi-robot ACS that consists of two components, a building material and autonomous robots. In our multi-robot ACS, an autonomous robot is capable of locating the building material in its environment, picking it up, transporting it, and attaching it to a structure. The multi-robot ACS is designed to be completely autonomous and capable of constructing three-dimensional structures. To test and evaluate our multi-robot ACS and its decentralized control strategy, we provide two implementations of our system. The primary implementation is realized using hardware and the secondary implementation is realized using simulation. Through the use of both implementations, we demonstrate how our decentralized control strategy can be used to coordinate the autonomous construction of three-dimensional structures. After discussing these demonstrations, we conclude this thesis by suggesting future research directions.